The Cash-Out Boundary: Why Retail Mobile-Money Acceptance Does Not Necessarily Reduce System-Wide Conversion Cost

Mobile-money adoption is often treated as evidence that an economy is becoming less dependent on cash. This paper isolates a narrower claim: consumer-to-merchant acceptance is insufficient to reduce system-wide cash-conversion cost when downstream digital reuse remains sparse. We define the cash-out boundary as the first point in a payment chain at which a balance cannot complete the holder's next intended transaction digitally. We derive exact finite-horizon expressions for cash-out dependence, retained digital value, circulation depth, and generalized cost in a four-stage consumer-merchant-supplier-worker network. The deterministic model is a scaffold: its monotonicity results follow from the construction. The substantive analysis applies documented public evidence as parameter anchors, propagates wide parameter uncertainty through the exact equations, and tests failure cases in which higher digital retention worsens welfare because fees, failures, or withdrawal restrictions are excessive. Across 120,000 uncertainty draws, retail digitization increases median circulation depth but leaves retained value after eight transaction opportunities close to zero. Meaningful retention emerges only when supplier, wage, and recurring household payment links are jointly available. The result is robust in direction but not universal in welfare: sufficiently high digital fees erase the generalized-cost advantage. The contribution is not the established idea that digital payments or interoperability matter. It is a precise separation between point-of-sale digitization and end-to-end balance reusability, together with exact metrics, failure bounds, and a reproducible model for measuring where the cash-out boundary movesVersion 2.0 substantially extends the original conceptual preprint with an exact finite-horizon model, evidence-anchored parameter uncertainty, failure-mode analysis, robustness checks, formal derivations, and a complete reproducibility package.